Vortex Dynamics in the Wake of Three Generic Types of Free-Stream Turbines Matthieu Boudreau, Guy Dumas To cite this version: Matthieu Boudreau, Guy Dumas. Vortex Dynamics in the Wake of Three Generic Types of Free- Stream Turbines. 16th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, Apr 2016, Honolulu, United States. hal-01891319 HAL Id: hal-01891319 https://hal.archives-ouvertes.fr/hal-01891319 Submitted on 9 Oct 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Vortex Dynamics in the Wake of Three Generic Types of Free-Stream Turbines Matthieu Boudreau1, Guy Dumas1* Abstract © ¨ An analysis of the vortex dynamics in the wake of three different free-stream turbine concepts is conducted § ¥ ¦ to gain a better understanding of the main processes affecting the energy recovery in their wakes. The £ ¤ ¢ turbine technologies considered are the axial-flow turbine (AFT), the cross-flow turbine (CFT), also ¡ known as the H-Darrieus turbine, and the oscillating-foil turbine (OFT). The analysis is performed on single turbines facing a uniform oncoming flow and operating near their optimal efficiency conditions at a Reynolds number of 107. Three-dimensional Delayed Detached-Eddy Simulations (DDES) are carried ISROMAC 2016 out using a commercial finite-volume Navier-Stokes solver. It is found that the wake dynamics of the International AFT is significantly affected by the triggering of an instability while that of the CFT and the OFT are Symposium on mainly governed by the mean flow field stemming from the tip vortices’ induction. Transport Keywords Phenomena and Turbine — Wake — Vortex dynamics — Axial-flow — Cross-flow — Oscillating-foil Dynamics of Rotating Machinery Hawaii, Honolulu April 10-15, 2016 1Laboratory LMFN, Department of Mechanical Engineering, Laval University, Québec, Canada *Corresponding author: [email protected] INTRODUCTION i.e., up to only 5 diameters downstream of the turbine. Several innovative renewable energy sources are being devel- Regarding the cross-flow turbines, several studies focused oped nowadays. Among them, the wind energy and the marine on the evolution of the shed vorticity and the tip vortices in current sectors are receiving a lot of attention because of their their wake and highlighted the fact that the tip vortices ejected great potential. Various turbine designs have been proposed from the CFT blades tend to convect toward the wake center in so far, including the well-known axial-flow turbine and the the spanwise direction [4, 5, 6, 7, 8, 9]. The same observation cross-flow turbine, as well as the oscillating-foil turbine. was also made more recently by Tescione et al. [10] who Despite the fact that a tremendous amount of work has used the PIV technique to observe in details the flow field already been devoted to the development of these technologies, in the near wake of an H-Darrieus CFT turbine. However, the vortex dynamics in turbines’ wakes at high Reynolds their measurements only covered the first three diameters numbers is very complex and is not fully understood yet. downstream of the turbine. Developing a better knowledge about this dynamics is crucial Deng et al. [11] showed qualitatively that the wake topology as it allows to gain better insights into the physics at play, of an oscillating cross-flow turbine operating at a Reynolds especially regarding the wake recovery. Cutting-edge Delayed number of 1,100 is strongly related to the blade’s aspect ratio. Detached-Eddy Simulations (DDES) of the three turbine Moreover, it is worth mentioning that the wakes of a flapping technologies mentioned above are carried out in this work to foil [12, 13] and that of a pitching panel [14, 15] used in the achieve this task. propulsion regime at low Reynolds numbers (Re ∼ 102 − 103) The axial-flow turbine’s wake has been analyzed by Sherry have both been found to widen in the transverse direction but et al. [1] who performed PIV measurements in the wake of a to contract in the spanwise direction, hence corroborating the turbine facing a uniform oncoming flow. They focused on the fact that the three-dimensional effects significantly affect the vortex instabilities occurring in the wake, which was found wake dynamics of an oscillating foil. However, no studies of to be strongly dependent on the tip speed ratio. Chamorro et the three-dimensional oscillating cross-flow turbine’s wake al. [2] also observed a similar instability in the wake of an have been conducted at high Reynolds numbers so far. AFT located in a turbulent boundary layer flow mimicking a marine boundary layer. The stereoscopic particle image The objective of the current work is to bring more light on velocimetry (SPIV) measurements of Lignarolo et al. [3] have the vortex dynamics observed in turbines wakes. A particular suggested that the enhanced mixing caused by the tip vortices’ emphasis is placed on how this dynamics affects the wake instability has a pronounced effect on the momentum recovery. recovery. The numerical methodology is presented in § 1 and However, their measurements were limited to the near wake, the results are shown and discussed in § 2. Vortex Dynamics in the Wake of Three Generic Types of Free-Stream Turbines — 2/12 1. METHODS 1.1 Geometric characteristics and operating pa- rameters The axial-flow turbine (AFT) [16, 17] is characterized by blades rotating at constant angular speed about an axis aligned with the direction of the flow. The cross-flow turbine (CFT) concept [18] also involves rotating blades except that they rotate around an axis perpendicular to the flow direction. The axis may be either horizontal or vertical, which explains why the name vertical-axis turbine is also commonly used to refer to cross-flow turbines. The blades of the oscillating-foil turbine (OFT) undergo both pitching and heaving motions in a plane perpendicular to the oncoming flow. These motions are constrained to be sinusoidal and the phase lag between both motions is enforced through a mechanical linkage making the turbine a one degree-of-freedom device [19]. Outlines of the three concepts are shown in Fig. 1. Note that the turbine’s characteristic length, D, is illustrated for each turbine concept. It corresponds to the turbine’s diameter in the case of the AFT and the CFT and to the overall extent of the blade motion in the case of the OFT. In this study, the operating conditions of the three turbine concepts have been chosen so that the turbines operate near their optimal efficiency conditions. The axial-flow turbine operates at a tip speed ratio (λ) of 3.5, defined as: ω D λ = , (1) 2 U∞ where ω is the turbine’s angular velocity and U∞ is the freestream velocity. The geometry of the AFT’s blades, based on a thicker version of the SD8020 profile, has been developed by the University of Victoria [20] in the context of a study for the Marine Energy Standards (TC114) [21]. The cross- flow turbine considered in this work is an H-Darrieus turbine Figure 1. Outline and main parameters of the axial-flow tur- consisting of simple straight blades. The rotating shaft and bine (top), the cross-flow turbine (middle) and the oscillating- connecting arms are not included in this study. More precisely, foil turbine (bottom) considered in this study. the CFT investigated corresponds to one of the single-bladed turbines studied by Gosselin et al. [22], which is characterized by a NACA0015 profile, a blade’s aspect ratio (b/c) of 15, a turbine’s characteristic length and the freestream velocity: diameter to chord length ratio of 7 and a tip speed ratio of 4.25. U∞ D Re = . (3) As shown in Fig. 1, the blade’s attach point x p is at the third D ν of the chord length. The OFT considered in this work has been chosen to correspond to the one analyzed by Kinsey & This value roughly corresponds to a middle-size turbine. How- Dumas [23] with a blade’s aspect ratio of 5, an overall extent ever, at such a high Reynolds number, the results presented of the blade motion to chord ratio D/c of 2.55 and operating in this study are expected to be essentially independent of at a reduced frequency ( f ∗) of 0.14, as defined by: an increase in the Reynolds number [24, 25]. The present observations and conclusions should therefore also apply to f c f ∗ = , (2) large-scale turbines. U∞ Note that the blade’s aspect ratio of the CFT is higher than where c is the chord length and f is the oscillation frequency of that of the OFT but the turbine’s aspect ratio (b/D) of these both sinusoidal motions, namely the pitching and the heaving two turbine concepts is very similar (b/D ≈ 2, see Fig. 1). motions. The distance between the leading edge of the blade and its attach point (x p) also corresponds to a third of the 1.2 Turbulence modeling chord length. To circumvent the limitations of the RANS approach for wake For comparison purposes, all three simulations have been flow simulation [26] and the prohibitive computational cost 7 conducted at a Reynolds number ReD of 10 based on the of a full LES simulation, we use in this study the Delayed Vortex Dynamics in the Wake of Three Generic Types of Free-Stream Turbines — 3/12 Detached-Eddy simulation (DDES) approach [27, 28].